Bernstein functions : theory and applications

Cover......Page 1
Title......Page 4
Copyright......Page 5
Preface to the second edition......Page 6
Preface......Page 7
Contents......Page 12
Index of notation......Page 14
1 Laplace transforms and completely monotone functions......Page 16
2 Stieltjes functions......Page 31
3 Bernstein functions......Page 36
4 Positive and negative definite functions......Page 50
5 A probabilistic intermezzo......Page 63
6.1 Representation of complete Bernstein functions......Page 84
6.2 Extended complete Bernstein functions......Page 95
7 Properties of complete Bernstein functions......Page 107
8 Thorin-Bernstein functions......Page 124
9 A second probabilistic intermezzo......Page 132
10 Transformations of Bernstein functions......Page 146
11.1 Special Bernstein functions......Page 174
11.2 Hirsch’s class......Page 187
12.1 The spectral theorem......Page 194
12.2 Operator monotone functions......Page 202
13.1 Semigroups and subordination in the sense of Bochner......Page 215
13.2 A functional calculus for generators of semigroups......Page 231
13.3 Subordination and functional inequalities......Page 248
13.4 Eigenvalue estimates for subordinate processes......Page 257
14 Potential theory of subordinate killed Brownian motion......Page 272
15.1 Inverse local time at zero......Page 283
15.2 First passage times......Page 300
16 Examples of complete Bernstein functions......Page 314
16.1 Special functions used in the tables......Page 315
16.2 Algebraic functions......Page 319
16.3 Exponential functions......Page 327
16.4 Logarithmic functions......Page 329
16.6 Hyperbolic functions......Page 345
16.7 Inverse hyperbolic functions......Page 351
16.8 Gamma and related special functions......Page 355
16.9 Bessel functions......Page 365
16.10 Miscellaneous functions......Page 373
16.11 CBFs given by exponential representations......Page 381
16.12.1 Entries 7–10, 12, 29–31, 40, 49–52, 57, 58, 60, 61......Page 386
16.12.3 Entries 80 and 81......Page 387
A.1 Vague and weak convergence of measures......Page 389
A.2 Hunt processes and Dirichlet forms......Page 392
Bibliography......Page 398
Index......Page 421